### Abstract

Original language | English |
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Publisher | ArXiv |

Number of pages | 41 |

Publication status | Published - 2018 |

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### Cite this

*Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators*. ArXiv.

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**Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators.** / Georgiadis, Athanasios; Kerkyacharian, Gerard; Kyriazis, George ; Petrushev, Pencho.

Research output: Working paper › Research

TY - UNPB

T1 - Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators

AU - Georgiadis, Athanasios

AU - Kerkyacharian, Gerard

AU - Kyriazis, George

AU - Petrushev, Pencho

PY - 2018

Y1 - 2018

N2 - We deal with homogeneous Besov and Triebel-Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel-Lizorkin spaces. Spectral multipliers for these spaces are established as well.

AB - We deal with homogeneous Besov and Triebel-Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel-Lizorkin spaces. Spectral multipliers for these spaces are established as well.

M3 - Working paper

BT - Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators

PB - ArXiv

ER -